Hi,
The "continuous line" you are observing in ListPlot is practically an interpolated function. you cannot "sample" more point then the original list, since ListPlot only store the originals. However you can always generate the interpolated line yourself
see the example below
(* generate a 101 points list *)
lis = Table[{t, Exp[-t]Sin[2 t]}, {t, 0, 5, 5/100.}]
(* ListPlot it and notice that it is sampled *)
ListPlot[lis]
(*interpolate it with a 6'th order polynomial *)
interpolated = Interpolation[lis, InterpolationOrder -> 6]
(* now the variable "interpolated" behaves like any other continuous function, but only in the range 0 to 5 *)
Plot[interpolated[t], {t, 0, 5}]

(* now you can sample the interpolated function
The line below gives you 5001 samples although the number of original samples was 101*)